Estimating expected excess returns using historical and option-implied volatility

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward-to-risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option-implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option-implied volatility risk measure yields a positive, but statistically insignificant, risk-return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal-to-noise ratio in the latter subperiod.